Modelling zero-inflated count data with a special case of the generalised poisson distribution

Abstract

A one-parameter version of the generalised Poisson distribution provided by Consul and Jain (1973) is considered in this paper. The distribution is uni- modal with a zero vertex and over-dispersed. A generalised linear model related to this distribution is also presented. Its parameters can be estimated by using a Fisher-Scoring algorithm which is equivalent to iteratively reweighted least squares. Due to its flexibility and capacity to describe highly skewed data with an excessive number of zeros, the model is suitable to be applied in insurance settings as an alternative to the negative binomial and zero-inflated model.